Straight LineEasy
Question
Let a and b be non-zero real numbers. Then, the equation (ax2 + by2 + c) (x2 - 5xy + 6y2) = 0 represents
Options
A.four straight lines, when c = 0 and a, b are of the same sign
B.two straight lines and a circle, when a = b, and c is of sign opposite to that of a
C.two straight lines and a hyperbola, when a and b are of the same sign and c is of sign opposite to that of a
D.a circle and an ellipse, when a and b are of the same sign and c is of sign opposite to that of a
Solution
(ax2 + by2 + c) (x2 - 5xy + 6y2) = 0
⇒ ax2 + by2 + c = 0 or x2 - 5xy + 6y2 = 0
⇒ x2 + y2 =
iff a = b, x - 2y = 0 and x - 3y = 0
Hence the given equation represents two straight lines and a circle, when a = b and c is of sign opposite to that of a.
⇒ ax2 + by2 + c = 0 or x2 - 5xy + 6y2 = 0
⇒ x2 + y2 =
iff a = b, x - 2y = 0 and x - 3y = 0Hence the given equation represents two straight lines and a circle, when a = b and c is of sign opposite to that of a.
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